With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are in...With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated. The main results are : 1) there exists only one global weak solution which continuously depends on initial value; 2) when t < T-0, the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.展开更多
Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, de...Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.展开更多
In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough num...In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough number of steps) of an associated homogeneous system is given.Finally,a sufficient condition for well-condi-tioning,intrinsically related to the problem data is proposed.展开更多
As second language learning becomes popular,various strategies to improve the learning process have been suggested.One of them includes the implantation of audiovisual materials(video authentic materials),which then l...As second language learning becomes popular,various strategies to improve the learning process have been suggested.One of them includes the implantation of audiovisual materials(video authentic materials),which then leads to a discussion of subtitle usage and the value of subtitles in second language learning.This essay focuses on searching for literature that suggests the value of subtitles,especially teletext subtitles,in improving second language learning.This was achieved by reviewing relevant research and experiments.The results suggested that even though uncertainty remained on what kind of materials fit what level of learners,in general,subtitles,especially teletext subtitles,were seen as a beneficial tool in developing learners' listening abilities and skills.展开更多
In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v,...In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincreasing on v for each x,u; there exists a constant q∈(0,1) such that t qf(x,t -1 u,tu)f(x,u,u)λ qf(x,λ -1 u,λu),0<t<1<λ, u∈R +. Then a necessary and sufficient condition for the equation u″+f(x,u,u)=0 on the boundary condition αu(a)-βu′(a)=0, γ(b)+δu′(b)=0 to have C 1(I) nonzero solutions is that 0<∫ b af(x,e(x),e(x))dx<∞, where α,β,γ,δ are nonnegative real numbers, Δ=(b-a)αγ+αδ+βγ>0, e(x)=G(x,x), G(x,y) is Green's function of above mentioned boundary value problem (when f(x,u,v)≡0). Received September 9,1996. Revised March 31,1997. 1991 MR Subject Classification: 34B.展开更多
By using fixed-point theorems, some new results for multiplicity of positive solutions for a class of second order m-point boundary value problem are obtained. The associated Green＇s function of this problem is also ...By using fixed-point theorems, some new results for multiplicity of positive solutions for a class of second order m-point boundary value problem are obtained. The associated Green＇s function of this problem is also given.展开更多
The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) o...The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) of piles. Based on a two-parameter,hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index(βsls) is obtained using the mean value first order second moment(MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation(MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement(slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety(FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.展开更多
By using fixed-point theorems, some new results for multiplicity of positive solutions for some second order m-point boundary value problems are obtained.The associated Green＇s function of these problems are also given.
In this paper we prove a uniqueness theorem of solutions for second boundary value problem of a class of second order nonlinear differential equation. In the proof the spectral theory of second order differential oper...In this paper we prove a uniqueness theorem of solutions for second boundary value problem of a class of second order nonlinear differential equation. In the proof the spectral theory of second order differential operators and Schauder's fixed point theorem are used.展开更多
Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these probl...Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.展开更多
A family of symmetric (hybrid) two step sixth P-stable methods for the accurate numerical integration of second order periodic initial value problems have been considered in this paper. These methods, which require on...A family of symmetric (hybrid) two step sixth P-stable methods for the accurate numerical integration of second order periodic initial value problems have been considered in this paper. These methods, which require only three (new) function evaluation per iteration and per step integration. These methods have minimal local truncation error (LTE) and smaller phase-lag of sixth order than some sixth orders P-stable methods in [1-3,10-11]. The theoretical and numerical results show that these methods in this paper are more accurate and efficient than some methods proposed in [1-3,10].展开更多
文摘With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated. The main results are : 1) there exists only one global weak solution which continuously depends on initial value; 2) when t < T-0, the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.
文摘Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.
基金This work has been partially supported by the "Generalitat Valenciana" grant GV1118/93the Spanish D. G. I. C. Y.T. grant PB93-0381
文摘In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough number of steps) of an associated homogeneous system is given.Finally,a sufficient condition for well-condi-tioning,intrinsically related to the problem data is proposed.
文摘As second language learning becomes popular,various strategies to improve the learning process have been suggested.One of them includes the implantation of audiovisual materials(video authentic materials),which then leads to a discussion of subtitle usage and the value of subtitles in second language learning.This essay focuses on searching for literature that suggests the value of subtitles,especially teletext subtitles,in improving second language learning.This was achieved by reviewing relevant research and experiments.The results suggested that even though uncertainty remained on what kind of materials fit what level of learners,in general,subtitles,especially teletext subtitles,were seen as a beneficial tool in developing learners' listening abilities and skills.
文摘In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincreasing on v for each x,u; there exists a constant q∈(0,1) such that t qf(x,t -1 u,tu)f(x,u,u)λ qf(x,λ -1 u,λu),0<t<1<λ, u∈R +. Then a necessary and sufficient condition for the equation u″+f(x,u,u)=0 on the boundary condition αu(a)-βu′(a)=0, γ(b)+δu′(b)=0 to have C 1(I) nonzero solutions is that 0<∫ b af(x,e(x),e(x))dx<∞, where α,β,γ,δ are nonnegative real numbers, Δ=(b-a)αγ+αδ+βγ>0, e(x)=G(x,x), G(x,y) is Green's function of above mentioned boundary value problem (when f(x,u,v)≡0). Received September 9,1996. Revised March 31,1997. 1991 MR Subject Classification: 34B.
文摘By using fixed-point theorems, some new results for multiplicity of positive solutions for a class of second order m-point boundary value problem are obtained. The associated Green＇s function of this problem is also given.
基金Projects(51278216,51308241)supported by the National Natural Science Foundation of ChinaProject(2013BS010)supported by the Funds of Henan University of Technology for High-level Talents,China
文摘The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) of piles. Based on a two-parameter,hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index(βsls) is obtained using the mean value first order second moment(MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation(MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement(slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety(FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.
基金the Natural Science Foundation of Anhui Educational Department(Kj2007b055) Youth Project Foundation of Anhui Educational Department(2007jqL101,2007jqL102)
文摘By using fixed-point theorems, some new results for multiplicity of positive solutions for some second order m-point boundary value problems are obtained.The associated Green＇s function of these problems are also given.
文摘In this paper we prove a uniqueness theorem of solutions for second boundary value problem of a class of second order nonlinear differential equation. In the proof the spectral theory of second order differential operators and Schauder's fixed point theorem are used.
基金sponsored by Natural Science Foundation of Anhui Educational Department(Kj2007b055) Youth Project Foundation of Anhui Educational Department (2007jqL1012007jqL102)
文摘Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.
基金State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation (PLN0115).
文摘A family of symmetric (hybrid) two step sixth P-stable methods for the accurate numerical integration of second order periodic initial value problems have been considered in this paper. These methods, which require only three (new) function evaluation per iteration and per step integration. These methods have minimal local truncation error (LTE) and smaller phase-lag of sixth order than some sixth orders P-stable methods in [1-3,10-11]. The theoretical and numerical results show that these methods in this paper are more accurate and efficient than some methods proposed in [1-3,10].
